Question

If the median and the range of four numbers {x, y, 2x + y, x – y}, where 0 < y < x < 2y, are 10 and 28 respectively, then the mean of the numbers is :

Answer 1

Answer:

14

Step-by-step explanation:

sice 0<y<x<2y

y>x/2

x-y<x/2

x-y<y<x<2x+y

median = (x+y)/2=10

x+y=20  eq (1)

range = (2x+y)-(x-y)=28

x+2y=28  eq(2)

from eq (1) and (2)

x=12 and y=8

mean=[(x-y)+y+x+(x+2y)]/4

mean=4x+y/4=56/4=14

Answer 2

Answer:

The mean of the numbers is 14.

Step-by-step explanation:

Since,

$y > \frac{x}{2} →x - y < \frac{x}{2}$

$x - y < y < x < 2x + y$

Hence median =

$\frac{x + y}{2} = 10$

$x + y = 20.......(i)$

And range =

$(2x + y) - (x - y) = x + 2y$

But range = 28

$x + y = 28.......(ii)$

From equation (i) and (ii),

$x = 12 \: and \: y = 8$

$Mean = \frac{(x - y) + y + x + (2x + y)}{4} = \frac{4x + y}{4} = x + \frac{y}{4} = 12 + \frac{8}{4} = 14$

The mean of the numbers is 14.